Question: Scarlett is playing a video game. She spends $900$ minerals to create $18$ workers. Each worker costs the same number of minerals. Write an equation to describe the relationship between $m$, the amount of minerals, and $w$, the number of workers.
Answer: Let's find the constant of proportionality. In the proportional relationship between $m$, the amount of minerals, and $w$, the number of workers, one constant of proportionality is the mineral cost per worker. It is the number we multiply by the number of workers to get the number of minerals. $w\,\times\, ?=m$ $\begin{aligned} w\,\times\, {?}&=m \\\\ {?}&=\dfrac{m}{w} \\\\ &=\dfrac{900}{18} \\\\ &={50} \end{aligned}$ The constant of proportionality is ${50}$. This means we can multiply ${50}$ by the number of workers to get the amount of minerals. Now, let's write the equation: $\begin{aligned} \text{amount of minerals}&={\text{minerals per worker}}\times\text{number of workers} \\\\ m&={50}w \end{aligned}$ One correct equation is: $m=50w$